class: center, middle, inverse, title-slide .title[ # Statistical Concepts Everyone Should Know ] .subtitle[ ## <p><em>Statistics for Life</em></p> ] .author[ ### <p><strong>John</strong><br /> <em>for</em> <strong>The John & Calvin Podcast</strong></p> ] --- class: inverse, center, large <h1 style="font-size: 100px; margin-top: 50px; font-family: Georgia, serif;">I</h1> <h1 style="font-size: 80px; margin-top: 75px;">Neutral Metrics</h1> <hr style="margin-top: 2em; margin-bottom: 2em;"> -- <h2 style="font-size: 50px;">Misuse and Misunderstandings Mislead</h2> -- <h2 style="font-size: 40px;">mean ≠ median</h2> --- ## 1. Neutral Metrics: Mean vs Median ### Local bar weath distribution: 50 Patrons <div id="htmlwidget-983315589fed18d622a7" style="width:750px;height:450px;" class="plotly html-widget"></div> <script type="application/json" 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Neutral Metrics: Mean vs Median ### Local bar weath distribution: 50 Patrons + Billon Gezos <div id="htmlwidget-6f1d8b9e786d9d3fe28d" style="width:750px;height:450px;" class="plotly html-widget"></div> <script type="application/json" 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style='color:#C04E3D'><b>Mean:<\/b><\/span> $2,941,235,622<br><span style='color:#BFA06D'><b>Median:<\/b><\/span> $59,505","showarrow":false,"align":"right","font":{"size":18,"color":"black"}}]},"config":{"doubleClick":"reset","modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"source":"A","attrs":{"92c97e03db3":{"x":{},"type":"bar"},"92c912f2b6cf":{"xintercept":{}}},"cur_data":"92c97e03db3","visdat":{"92c97e03db3":["function (y) ","x"],"92c912f2b6cf":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> --- ## 1. Neutral Metrics: Mean vs Median <div style="font-size: 130%; text-align: left; margin: 100px 0;"> <p><strong>Mean</strong>: Sum of all values divided by the number of values.</p> <br> <p><strong>Median</strong>: Middle value when the values are ordered.</p> </div> --- ## 1. Neutral Metrics: Mean vs Median ### Impact of a $150B Outlier on Mean vs. Median — Across Sample Sizes <table class="table" style="font-size: 24px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:right;"> Sample Size </th> <th style="text-align:right;"> Mean </th> <th style="text-align:right;"> Median </th> </tr> </thead> <tbody> <tr> <td style="text-align:right;"> 101 </td> <td style="text-align:right;padding-left: 20px;"> $1,485,214,194 </td> <td style="text-align:right;padding-left: 20px;"> $61,587 </td> </tr> <tr> <td style="text-align:right;"> 1,001 </td> <td style="text-align:right;padding-left: 20px;"> $ 149,915,313 </td> <td style="text-align:right;padding-left: 20px;"> $60,141 </td> </tr> <tr> <td style="text-align:right;"> 10,001 </td> <td style="text-align:right;padding-left: 20px;"> $ 15,063,285 </td> <td style="text-align:right;padding-left: 20px;"> $59,610 </td> </tr> <tr> <td style="text-align:right;"> 100,001 </td> <td style="text-align:right;padding-left: 20px;"> $ 1,564,864 </td> <td style="text-align:right;padding-left: 20px;"> $59,897 </td> </tr> <tr> <td style="text-align:right;"> 1,000,001 </td> <td style="text-align:right;padding-left: 20px;"> $ 214,846 </td> <td style="text-align:right;padding-left: 20px;"> $59,868 </td> </tr> <tr> <td style="text-align:right;"> 10,000,001 </td> <td style="text-align:right;padding-left: 20px;"> $ 79,864 </td> <td style="text-align:right;padding-left: 20px;"> $59,885 </td> </tr> <tr> <td style="text-align:right;"> 100,000,001 </td> <td style="text-align:right;padding-left: 20px;"> $ 66,365 </td> <td style="text-align:right;padding-left: 20px;"> $59,876 </td> </tr> </tbody> </table> --- ## 1. Neutral Metrics: Mean vs Median A more realistic example  --- .pull-left[ ### Economics & Wealth - GDP per capita - household income - net worth - home price - monthly rent - CEO compensation ### Health & Healthcare - life expectancy - healthcare spending per person - hospital bill - patient out-of-pocket cost ] .pull-right[ ### Academics - test score (SAT, PISA) - GPA - academic citations - speaking invitations per expert ### Other - commute time - screen-time per user - household energy use - carbon emissions per capita - YouTube ad revenue per channel - revenue per app in the App Store - Software Bug Fix Times ] --- ## 1. Neutral Metrics: Mean vs Median ### Pareto Distribution <div id="htmlwidget-dcdfc64296f5794e54a4" style="width:750px;height:450px;" class="plotly html-widget"></div> <script type="application/json" 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Neutral Metrics: Mean vs Median ### Normal Distribution <div id="htmlwidget-cbd3ad10bd2d35a2e76d" style="width:750px;height:450px;" class="plotly html-widget"></div> <script type="application/json" 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style='color:#C04E3D'><b>Mean:<\/b><\/span> $90,086<br><span style='color:#BFA06D'><b>Median:<\/b><\/span> $90,024","showarrow":false,"align":"right","font":{"size":18,"color":"black"}}]},"config":{"doubleClick":"reset","modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"source":"A","attrs":{"92c9390cc8a7":{"x":{},"type":"bar"},"92c976496933":{"xintercept":{}},"92c94d99cff0":{"xintercept":{}}},"cur_data":"92c9390cc8a7","visdat":{"92c9390cc8a7":["function (y) ","x"],"92c976496933":["function (y) ","x"],"92c94d99cff0":["function (y) 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Neutral Metrics <span style="font-size: 32px;"> A metric is just a calculated number. </span> <br> <span style="font-size: 32px;"> It can be misused, but only if its not understood. <br> <br> <br> </span> -- <span style="font-size: 32px;"> To understand any metric, you must know: </span> <ul style="font-size: 26px; line-height: 1.4;"> <li>how it's calculated</li> <li>the assumptions it relies on</li> <li>the <b>distribution</b> of the data</li> </ul> --- class: inverse, center, large <h1 style="font-size: 100px; margin-top: 50px; font-family: Georgia, serif;">II</h1> <h1 style="font-size: 80px; margin-top: 75px;">Distributions</h1> <hr style="margin-top: 2em; margin-bottom: 2em;"> -- <h2 style="font-size: 55px;">What's Typical, What's Rare, What's Extreme</h2> <h2 style="font-size: 40px;">Theoretically</h2> --- ## 2. Distributions ### Theoretical models of where values are likely to occur - **Symmetry vs. Skewness** Are values evenly spread around the center, or do they stretch more in one direction? - **Variability (Spread)** How tightly or widely are the values clustered? - **Tail Behavior** How likely are extreme or outlier values? --- ## 2. Distributions ### Theoretical models of where values are likely to occur <div id="htmlwidget-f25d4e1770d66a86dcce" style="width:750px;height:450px;" class="plotly html-widget"></div> <script type="application/json" 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(y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> ---  ---  --- ## 2. Distributions $$ f(x) = \frac{1}{\sigma \sqrt{2\pi}} \, e^{ -\frac{1}{2} \left( \frac{x - \mu}{\sigma} \right)^2 } $$ Where: - `\(\mu\)` = the **mean** (center) - `\(\sigma\)` = the **standard deviation** (spread) - `\(x\)` = the value at which we evaluate the density - `\(f(x)\)` = the probability density at `\(x\)` given `\(\mu\)` and `\(\sigma\)` --- .center[ **Normal distribution** ] $$ f(x) = \frac{1}{\sigma \sqrt{2\pi}} \, e^{ -\frac{1}{2} \left( \frac{x - \mu}{\sigma} \right)^2 } $$ <hr style="border: 0; height: 1px; background: lightgray;"> <div style="text-align: center;"> <img src="assets/normal_annotated.png"> </div> --- ## 2. Distributions <span style="font-size: 32px;"> A distribution defines what's typical, what's rare, and what's extreme in a dataset. </span> <br> -- <span style="font-size: 32px;"> Identifying the distribution helps you understand: </span> <ul style="font-size: 26px; line-height: 1.4;"> <li>what outcomes are likely and unlikely</li> <li>how much variation or uncertainty exists</li> <li>whether rare or extreme events fall within expectations</li> <li>if deviations from expectations signal a need for more investigation</li> </ul> -- <br> <span style="font-size: 26px;"> Distributions describe single variables. What about relationships between variables? </span> --- class: inverse, center, large <h1 style="font-size: 100px; margin-top: 50px; font-family: Georgia, serif;">III</h1> <h1 style="font-size: 80px; margin-top: 75px;">Correlation, Confounding, Causation</h1> <hr style="margin-top: 2em; margin-bottom: 2em;"> -- <h2 style="font-size: 80px;">and the Stories We Tell</h2> --- class: inverse, center, large, middle <h1 style="font-size: 80px; ">Correlation</h1> ---  ---  --- class: inverse, center, large, middle <h1 style="font-size: 80px; ">Confounding</h1> --- .pull-left[ <div class="plotly html-widget html-fill-item" id="htmlwidget-fbfc52d82635d988c6e1" style="width:360px;height:288px;"></div> <script type="application/json" 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Oil (g/day)","yaxis":"y","line":{"color":"black","width":5},"marker":{"color":"rgba(255,127,14,1)","line":{"color":"rgba(255,127,14,1)"}},"error_y":{"color":"rgba(255,127,14,1)"},"error_x":{"color":"rgba(255,127,14,1)"},"xaxis":"x","frame":null},{"x":[1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020],"y":[20,21,25,30,40,40,50,55,57,60,63,65,70,80,90,90,100,110,115,120,120,130,145,150,160,165,175,188,200,220,225,230,240,250,255,270,290,310,325,345,355,360,375,385,390,400,410,420,430,440,460,480,505,540,550,570,585,590,595,600,620,630,640,650,660,670,685,695,705,715,720,730,740,735,740,730,720,715,710,715,720,725,735,740,750,760,770,760,765,765,760,750,735,725,710,715,720,730,725,725,720,720,710,710,705,700,685,670,655,640,630,615,610,600,600,605,605,605,610,610],"type":"scatter","mode":"lines","name":"Heart Disease Deaths (thousands)","yaxis":"y2","line":{"color":"red","width":5},"marker":{"color":"rgba(44,160,44,1)","line":{"color":"rgba(44,160,44,1)"}},"error_y":{"color":"rgba(44,160,44,1)"},"error_x":{"color":"rgba(44,160,44,1)"},"xaxis":"x","frame":null}],"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.20000000000000001,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script> <small style="font-size:12px; line-height:1.1; display:inline-block;"> "Figure 2 correlates saturated fat and total vegetable oil consumption versus heart disease deaths in the U.S.A., with data on all three dating back to at least 1909."</small> <small style="font-size:12px; line-height:1; display:inline-block;"> Data: <a href="https://www.fns.usda.gov/cnpp/us-foodsupply/nutrient-content-1909-2010">USDA Food Supply</a> | Paper: <a href="https://www.sciencedirect.com/science/article/abs/pii/S0306987717305017?via%3Dihub">ScienceDirect</a> | Video: <a href="https://www.youtube.com/watch?v=7kGnfXXIKZM">YouTube</a> </small> --- ## 3. Correlation, Confounding, Causation <span style="font-size: 28px;">Not all patterns point to cause-and-effect. </span> <br> -- <span style="font-size: 28px;"> To understand relationships between variables, consider: </span> <ul style="font-size: 22px; line-height: 1.4;"> <li>Correlation could mean nothing, or it could mean a lot.</li> <li>It could even confuse or obscure real relationships.</li> <li>Causality can be tested (<b>carefully</b>).</li> <li>Are we just building stories we want to tell?</li> </ul> <br> -- <span style="font-size: 26px;"> If variables are related, what pattern does that relationship follow? </span> --- class: inverse, center, large <h1 style="font-size: 100px; margin-top: 50px; font-family: Georgia, serif;">IV</h1> <h1 style="font-size: 80px; margin-top: 75px;">Shapes of Change</h1> <hr style="margin-top: 2em; margin-bottom: 2em;"> -- <h2 style="font-size: 60px;">What Curve, What Point?</h2> --- ## 4. Shapes of Change <div id="htmlwidget-fbc9973e359619ea20b8" style="width:750px;height:500px;" class="plotly html-widget"></div> <script type="application/json" 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Shapes of Change <span style="font-size: 28px;">Depending on context, changes in inputs to outputs can be very different.</span> <br> -- <span style="font-size: 28px;">Recognizing the shape of change helps you understand: </span> <ul style="font-size: 22px; line-height: 1.4;"> <li>whether progress will be steady or accelerating</li> <li>when gains may slow down or speed up unexpectedly</li> <li>how small inputs can sometimes create outsized effects, or hit limits</li> </ul> -- <span style="font-size: 24px;">Early in the process, it’s hard to tell which curve you're on. Misjudging it can lead to frustration or unrealistic expectations.</span> -- <br> <span style="font-size: 24px;">Our expectations shape how we interpret new information.</span> --- class: inverse, center, large <h1 style="font-size: 100px; margin-top: 50px; font-family: Georgia, serif;">V</h1> <h1 style="font-size: 80px; margin-top: 75px;">Bias</h1> <hr style="margin-top: 2em; margin-bottom: 2em;"> -- <h2 style="font-size: 60px;">Expectations and Reality</h2> --- ## 5. Bias **Bias** is the difference between the expected value of an estimator and the true value of the parameter it estimates. Formally: $$ \text{Bias}(\hat{\theta}) = \mathbb{E}[\hat{\theta}] - \theta $$ Where: - `\(\hat{\theta}\)` = the **estimator** (your calculated estimate) - `\(\theta\)` = the **true parameter** (the real value you want) - `\(\mathbb{E}[\hat{\theta}]\)` = the **expected value** of the estimator (its long-run average over many samples) - If Bias = 0 → the estimator is **unbiased**. - If Bias ≠ 0 → the estimator is **biased** (systematically too high or too low). --- Bias doesn't just shift your first guess. It filters what you see next — making you even more biased over time Selection bias: The sample is not representative of the population. Omitted variable bias: Leaving out a variable that influences both the dependent and independent variables. Measurement bias (or information bias): Errors in how data is collected or recorded. Survivorship bias: Only analyzing "survivors" or those who remain, ignoring those who dropped out or failed. Recall bias: Errors because people remember things inaccurately (common in surveys and retrospective studies). Observer bias: Researcher's expectations subtly influence measurements or observations. Publication bias: Studies with "positive" results are more likely to be published than "null" or "negative" results. --- ## 5. 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Bias <span style="font-size: 28px;">Our minds filter reality through prior beliefs and assumptions, or <b>bias</b>.</span> <br> <span style="font-size: 28px;">Recognizing bias helps you understand: </span> <ul style="font-size: 20px; line-height: 1.2;"> <li>how it can shape attention and memory</li> <li>why we favor evidence that fits what we already believe</li> <li>how feedback loops can reinforce or shift our views over time</li> <li>how bias can escalate, growing from subtle differences in interpretation to extreme positions over time</li> </ul> -- <span style="font-size: 22px;">Without awareness, bias can change how we see the world, gradually strengthening and pushing us further from reality.</span> -- <span style="font-size: 22px;">From time to time ask yourself:</span> >Where am I on the Bias Escalation Curve? --- <h1 style="margin-bottom: 0em;">Neutral Metrics</h1> <h4 style="margin-top: 0; font-weight: bold;">Misuse and Misunderstandings Mislead</h2> <h1 style="margin-bottom: 0em;">Distributions</h1> <h4 style="margin-top: 0; font-weight: bold;">What's Typical, What's Rare, What's Extreme - Theoretically</h2> <h1 style="margin-bottom: 0em;">Correlation, Confounding, Causation</h1> <h4 style="margin-top: 0; font-weight: bold;">and the Stories We Tell</h2> <h1 style="margin-bottom: 0em;">Shapes of Change</h1> <h4 style="margin-top: 0; font-weight: bold;">What Curve, What Point</h2> <h1 style="margin-bottom: 0em;">Bias</h1> <h4 style="margin-top: 0; font-weight: bold;">Expectations and Reality</h2>